#### Topic Content:

- The Converse of Statement
- Equivalent Statements

### The Converse of Statement:

Let A → B be an implication, then the converse of A → B is B → A

### Equivalent Statements:

Let the implication X → Y be true, if Y → X is true, then X and Y are said to be equivalent statements. Thus, we write and say that X ↔ Y is a **bi-implication**.

### Example 7.6.1:

Given the statements:

P_{1}: The teacher entered and started the lesson

P_{2}: Either it will rain tomorrow or the visit will take place, or it will rain tomorrow and the visit will take place anyway.

Use appropriate symbols and truth tables to describe:**1. **The conditions for P_{1} to be true,**2.** The conditions under which P_{2} will be false

**Solution:**

**1.** Let the sub-statements be

A: the teacher entered

B: the teacher started the lesson

If P_{1} is true, then A → B is true.

Recall, the relation “and” which suggests both A and B must true before A → B could be true

**Truth table**

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